Final answer:
To compute a 98% confidence interval for the mean number of pounds of trash per person per week in the city, we use a t distribution. The margin of error is found by multiplying the critical value with the standard error, and the confidence interval is calculated by adding and subtracting the margin of error from the sample mean. In this case, the confidence interval is (32.734, 36.866).
Step-by-step explanation:
To compute a 98% confidence interval for the mean number of pounds of trash per person per week generated in the city, we will use the t distribution. First, we need to determine the margin of error, which is the critical value multiplied by the standard error. The critical value can be found using a t-table, with the degrees of freedom equal to the sample size minus one. In this case, the critical value is approximately 2.615. The standard error is the standard deviation divided by the square root of the sample size. Plugging in the values, we find the margin of error to be approximately 2.066.
To find the confidence interval, we take the sample mean and add or subtract the margin of error. The sample mean is 34.8 pounds. Adding and subtracting the margin of error gives us a confidence interval of (32.734, 36.866). This means that we are 98% confident that the true mean number of pounds of trash per person per week in the city falls within this range.